It was not a latency issue that caused the problem. I was able to get my site ownership verified once I used the second option for URL prefix property offered under the html tag option. I pasted the "meta tag" Google provided to complete verification. Afterwards, only a long mixed-case alphanumeric string shows, not the meta tag.

Given how important it is to have Substacks connected to Google Search, I believe a simpler site verification process would be beneficial. Substack is an essentially-closed system that does not accept code snippets like CGNP's website based on WordPress.